Question: Solve for $x$ : $2x^2 - 2x - 180 = 0$
Solution: Dividing both sides by $2$ gives: $ x^2 {-1}x {-90} = 0 $ The coefficient on the $x$ term is $-1$ and the constant term is $-90$ , so we need to find two numbers that add up to $-1$ and multiply to $-90$ The two numbers $-10$ and $9$ satisfy both conditions: $ {-10} + {9} = {-1} $ $ {-10} \times {9} = {-90} $ $(x {-10}) (x + {9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -10) (x + 9) = 0$ $x - 10 = 0$ or $x + 9 = 0$ Thus, $x = 10$ and $x = -9$ are the solutions.